Going to word this question a bit more straightforward than I may have before. Also, I'm trying to use baby formulas so I can grasp exactly what's going on.

Object A has an elasticity of Y, and is propped against an effectively immobile rigidbody.

Object B is a rigidbody with mass M, and is colliding against Object A perpendicularly. Various Object B's may have a different shape by which to strike Object A. Some may be flat and apply strain uniformly across the whole of Object A, while some may be sharp and concentrate the strain in a smaller area.

I'm trying to figure out how quickly Object A's stress accelerates Object B in the opposite direction. f=ma has been thrown to me, but I'm a very visual person and don't exactly see where f is coming from. Intuition tells me that the collision area is important, and that the only area of Object A that matters is what's in the immediate collision area.

Is it simply Object A's stress multiplied by the area of impact?
And would it in-turn effectively accelerate Object B at a rate of stress/mass/sec^2?

The practical answer is that you use a finite element analysis package. If you don't want to go to that trouble, then you model both bodies as simple springs (the spring constants come from the stress-strain moduli and the geometry of the situation; engineering texts will be more helpful than physics texts in this step) and proceed straight ahead. There is no exotic physics here, just complicated set ups. The complexity of the number of different problems is why there are no list of formulas.
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dmckee♦Jan 28 '13 at 17:01

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You don't need to use finite elements per se. That just happens to be the most common structural analysis technique. But there are other methods (finite difference, finite volume, Eulerian, Lagrangian, Arbitrary Eulerian-Lagrangian, etc...). Computational structural mechanics is what you're after either way.
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tpg2114Jan 29 '13 at 5:44